1/1*2+1/2*3+1/3*4+1/4*5+…+1/199*200怎样解

1/1*2+1/2*3+1/3*4+1/4*5+…+1/199*200怎样解
1/1*2+1/2*3+1/3*4+1/4*5+…+1/199*200怎样解

1/1*2+1/2*3+1/3*4+1/4*5+…+1/199*200怎样解
=（1-1/2）+（1/2-1/3）+（1/3-1/4）+（1/4-1/5）+.+(1/198-1/199)+(1/199+1/200)
=1-1/200
=199/200

1/1*2+1/2*3+1/3*4+1/4*5+…+1/199*200
=1/1-1/2 +1/2-1/3+1/3-1/4+.......-1/199+1/199-1/200
=1-1/200
=199/200

裂项
原式=1/1 - 1/2 + 1/2 - 1/3 +...+1/199 - 1/200 = 1/1 - 1/200 = 199/200